Flash Gordon was the hero of a science fiction adventure, a rocket ship pilot, that first appeared in comic strip form in 1934. The story was intended to compete with a comic called Buck Rogers. The story went on to be dramatized in serial films, radio, television, and animated series.
Leon Mandrake was a Canadian magician (1911-1993), but Yossarian is probably comparing himself to a comic strip character, “Mandrake the Magician,” a specialist in hypnotic technique, who debuted in 1933 and continued to run as a color comic strip for the rest of the century -- also making appearances on radio and in films, theater, and television.
Bill Shakespeare was an English playwright.